Birefringent optical materials exhibit a refractive index that varies with the direction of polarization of the incident light, and are characterized by the difference between the maximum and minimum values of the refractive index, and by the directions of polarization along principal axes corresponding to these extreme values. Retardation is the phase difference introduced between waves polarized along the principal axes resulting from travel through the birefringent material, and is proportional to the birefringence, the distance traveled by the light through the material, and to the frequency of the light. It may be expressed in “waves” at some given wavelength; that is, a phase difference of 2π radians times the number of “waves” at the given (vacuum) wavelength.
Isotropic materials such as fused silica and microcrystalline ZnSe are not birefringent, but can be induced to become birefringent by external factors, such as mechanical stress. This is known as the photoelastic effect. In an isotropic material, a strain (and the associated stress) along one direction causes the refractive index along that direction to change from the refractive index along a perpendicular direction and also from the refractive index in the absence of strain. These directions are the principal axes associated with the stress-induced birefringence. Linearly polarized light experiences one or the other value of the refractive index depending on whether its direction of polarization is parallel to or perpendicular to the direction of the strain. For intermediate directions of polarization, the electromagnetic wave can be resolved into two components along the principal axes, each component propagating with a phase velocity corresponding to the refractive index it experiences. This difference in phase velocity results in a phase difference (retardation) between the two components. When recombined, this results in a change of the state of polarization of the resulting light (See, e.g., “Piezo-Optical Birefringence Modulators: New Use for Long Known Effect” by J. C. Kemp, J. Opt. Soc. Am. 59, 950-954 (1969).).
Photoelastic modulators (PEMs) are optical devices that use the photoelastic effect to generate a time-dependent birefringence which can be used for modulating: (i) the state of polarization of light; or (ii) light intensity. Piezoelectric transducers (PZTs) may be used to apply mechanical stress to normally nonbirefringent materials. Since they have no internal moving parts, PZTs can operate at high frequencies; however, only small displacements may be generated at high-frequencies of operation (using reasonable driving voltages), unless resonant PEMs are used where small driving forces applied at the resonance frequency of the PEM may generate high stress oscillation amplitudes in the PEM (See, e.g., J. C. Kemp, supra.).
Conventional applications of PEMs require small retardation amplitudes, typically less than one wave at a specified wavelength (fused silica PEMs in the visible, and ZnSe, Ge, and Si in the infrared, as examples). A PEM having a retardation amplitude of a quarter-wave will convert linearly polarized incident light into circularly polarized light (alternatively right- and left-polarized at the peaks and troughs of the retardation), passing through elliptical polarizations between these polarizations. If a quarter-wave plate (which adds a fixed retardation of a quarter-wave) is introduced into the optical path, the total retardation (PEM plus plate) will oscillate between zero and one half-wave and, if properly oriented polarizers are placed on both sides of the optical system, the intensity of the emerging light will oscillate between zero and the incident intensity, thereby generating high-speed intensity modulation for monochromatic light. See, for example, “Photoelastic Modulators” a publication of HINDS Instruments, Inc. of Hillsboro, Oreg., wherein a rectangular bar of transparent photoelastic material is attached to a piezoelectric transducer such that the bar vibrates along its long dimension and the maximum of the oscillating birefringence effect is maximum at the center of the fused silica bar.
The input polarizer is assumed to be at 45° relative to the optical axes of the PEM, while the output polarizer can be either parallel, or perpendicular, to the input polarizer.
An interferometer may be constructed by introducing a phase difference between two linearly polarized optical waves with mutually orthogonal directions of polarization, and translating this difference into a light intensity value by means of a photoelastic modulator disposed between two polarizers, as described hereinabove. Such an interferometer can be used in a Fourier transform (FT) spectrometer (PEM/FT) (See, e.g., U.S. Pat. No. 4,905,169 for “Method And Apparatus For Simultaneously Measuring Fluorescence Over A Multiplicity Of Spectral Channels” which issued to Tudor N. Buican and John C. Martin on Feb. 27, 1990.).
PEM/FT spectrometers are capable of providing greater than 105 interferograms/spectra scanned per second, as opposed to a few thousand scans/s available with the fastest non-PEM interferometers; however, achieving spectral resolutions useful in the mid-infrared (smaller than tens of cm−1) is difficult. If individual PEMs are stacked together and are driven in phase in order that their retardation amplitudes are added, spectral resolutions of less than 10 cm−1 should be achievable with multiple passes therethrough (See, e.g., U.S. Pat. No. 6,970,278 for “Controlling Resonant Photoelastic Modulators” which issued to Tudor N. Buican on Nov. 29, 2005.). However, because of light losses at the optical interfaces, such a system has a limited light throughput (estimated by the present inventor to be between 3-8%) which limits its usefulness in applications where the intensity of the light to be analyzed is low. This limitation may not be important in applications where either a high-intensity light source is available, or large-aperture collection optics can be used. However, in some applications, the intensity of the available light is small and few photons can be captured in the short time available to an ultra-high-speed instrument.
As a solution to this problem, the PEM may be fabricated out of a single, bar-shaped piece of optical material having suitable size and shape to replace an entire stack of individual PZT-driven PEMs. This may be thought of as bringing together the PEMs in the stack until they touch, and then removing the interfaces between touching windows, thereby leaving a bar of optical material with multiple PZTs positioned along its length, and with the light traveling along the long axis of the bar. However, this approach fails where the equivalent of the individual windows are no longer physically separated, but rather are in direct contact with each other in the bar, since elastic waves can now travel along the length of the bar. That is, the compression waves which travel from the PZTs perpendicular to the direction of light propagation will also propagate as elastic waves along the length of the bar in the direction of light propagation. Since the stresses in the elastic wave will integrate to zero over a full wavelength (period) of this wave, the only contribution to total retardation will come from the remainder of less than one wavelength from the division of the bar length by the wavelength of the elastic wave. In fact, the maximum contribution from an elastic wave propagating along the bar is that of one-half of its wavelength (since that gives the maximum integrated retardation, which then gradually falls to zero as the remainder increases beyond a half-wavelength of the elastic wave to a full wavelength, and subsequently repeats this oscillatory pattern as the total length of the bar continues to increase). Therefore, the retardation does not increase beyond this limit if the bar length is increased.
The same result obtains if a standing elastic wave is set up along the length of the bar, since the interfering elastic waves propagate through the points of zero amplitude (nodes), so that adjacent antinodes always oscillate with opposite phases. Consequently, the retardation integrates to zero over the length of two adjacent antinodes; that is, twice the separation between adjacent nodes, or one wavelength. The maximum total retardation along the bar axis is obtained for an odd number of antinodes; that is, the integral over the distance between two adjacent nodes, or one-half of a wavelength. Resonant standing elastic waves along the length of the bar created by reflection at the ends of the bar do not change this conclusion.
Although the bar in this invention is a three-dimensional (3-D) object, it operates as a waveguide for elastic waves which exhibit propagating modes only along the length of the bar. Therefore, the bar and the elastic waves propagating therein behave as if they were a one-dimensional (1-D) system: therefore, the phrase “essentially 1-D”, as used throughout the Specification and claims, denotes this approximation (See, B. A. Auld, Acoustic Fields And Waves In Solids, Vol. II, 2nd Ed., Krieger Publishing Co., 1990.)
Low retardation, bar-shaped PEMs using birefringence generated from a standing elastic wave along the length of the bar where the path of the light propagating through the bar and perpendicular to its long axis, has been deliberately placed a distance from the vicinity of the PZTs and the perturbing static birefringence caused by static stresses due, for example, to affixing the PZTs to the optical element, are known. See, for example, “New Design For A Photoelastic Modulator” by J. C. Canit and J. Badoz, App. Opt. 22, pp. 592-594 (1983); “Low Frequency Photoelastic Modulator” by J. C. Canit and C. Pichon, App. Opt. 23, pp. 2198-2200 (1984); and D. Yang et al. in “Photoelastic Modulator: Polarization Modulation And Phase Modulation, J. Opt. (Paris) 26, pp. 151-159 (1995).